Contact person: Research and Java Implementation -- 2

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Location: Vienna, Austria

Budget: Recommended by industry experts

Time to start: As soon as possible

Project description:
"The aim of this thesis is to gain a deeper mathematical understanding of Schoof’s algorithm and to develop a working implementation in Java. Furthermore, the thesis demonstrates how the algorithm can be applied in practice. To this end, all necessary mathematical foundations are thoroughly explained, with a particular focus on the structure of elliptic curves over finite fields, the role of the Frobenius endomorphism, and the application of the Chinese Remainder Theorem. Schoof’s algorithm is presented step by step through carefully chosen examples in order to bridge the theoretical foundations with practical applicability.
In the next stage, the algorithm is implemented in Java. The focus lies on the correct representation of mathematical structures, modular arithmetic, and the efficient implementation of polynomial operations. The results are validated using selected elliptic curves over small finite fields and compared with the expected outcomes. Finally, the thesis highlights the role of Schoof’s algorithm in the context of elliptic curve cryptography. It discusses the limitations of the algorithm, its potential applications, and already established alternatives." (client-provided description)